Solve for $x$ and $y$ using elimination. $\begin{align*}3x+2y &= -9 \\ -4x-y &= 5\end{align*}$
Explanation: We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $1$ and the bottom equation by $2$ $\begin{align*}3x+2y &= -9\\ -8x-2y &= 10\end{align*}$ Add the top and bottom equations. $-5x = 1$ Divide both sides by $-5$ and reduce as necessary. $x = -\dfrac{1}{5}$ Substitute $-\dfrac{1}{5}$ for $x$ in the top equation. $3( -\dfrac{1}{5})+2y = -9$ $-\dfrac{3}{5}+2y = -9$ $2y = -\dfrac{42}{5}$ $y = -\dfrac{21}{5}$ The solution is $\enspace x = -\dfrac{1}{5}, \enspace y = -\dfrac{21}{5}$.